Question: What's the first wrong statement in the proof below that $ \triangle EBD \cong \triangle EBC$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \overline{EF} \cong \overline{BE}$ $, \ $ $ \angle CEF \cong \angle BED$ $, \ $ $ \angle ECF \cong \angle BDE$ $, \ $ $ \overline{AB} \cong \overline{BE}$ $, \ $ $ \angle BAC \cong \angle BED$ $, \ $ and $\ $ $ \overline{AC} \cong \overline{DE}$ Proof $ \triangle EBD \cong \triangle EFC$ because AAS $ \overline{DE} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \angle BCE \cong \angle CEF$ because alternate interior angles are equal $ \overline{EF} \cong \overline{AC}$ because corresponding parts of congruent triangles are congruent $ \triangle ABC \cong \triangle EBD$ because SAS $ \triangle EBD \cong \triangle EBC$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{AC} \cong \overline{EF}$ is the first wrong statement.